Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions

Abstract

We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature $T_c$, the disorder and thermally averaged correlation function $B(r)$ of the phase field $\theta (x)$, $B(r)=\overline{<[\theta (x)-\theta (x+r){]}^2>}$ behaves, for $r\gg a$, as $B(r)\simeq A(\tau ){\ln }^2(r/a)$ where $r=|r|$ and $a$ is a microscopic length scale. We derive the RG equations up to cubic order in $\tau =(T_c-T)/T_c$ and predict the universal amplitude $A(\tau )=2{\tau }^2-2{\tau }^3+\mathcal{O}({\tau }^4)$. The universality of $A(\tau )$ results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute $A(\tau )$ numerically and obtain a remarkable agreement with our analytical prediction, up to $\tau \approx 0.5$.

5 pages, 3 figures

References in corpus (4)

• Gaussian Statistics of Fracture Surfaces
• Domain walls and chaos in the disordered SOS model
• Disordered free fermions and the Cardy Ostlund fixed line at low temperature
• Super-rough phase of the random-phase sine-Gordon model: Two-loop results

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